Question

using trig to find angles
score: 0/2 penalty: none
question
solve for ( x ). round to the nearest tenth of a degree, if necessary.
answer attempt 1 out of 2
( x = )

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the sine of an angle \(x\) is defined as \(\sin x=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the side opposite to angle \(x\) is \(IH = 4.1\) and the hypotenuse is \(IG=9.5\). So, \(\sin x=\frac{4.1}{9.5}\).

Step2: Calculate the value of \(x\)

We know that if \(\sin x = a\), then \(x=\sin^{- 1}(a)\). Substitute \(a = \frac{4.1}{9.5}\approx0.4316\). Using a calculator, \(x=\sin^{-1}(0.4316)\).

$$x\approx25.6^{\circ}$$

Answer:

\(25.6\)